If I've watched it once, I've watched it a thousand times. The Pathé newsreel, with the sepia tone and the comical Cholmondley-Warner voiceover. The West Indian with the sad eyes trudging from door to door. And the pan shot on the sign that perhaps explains the sad eyes. NO BLACKS, NO IRISH.

We have come a long way since then, but making Britain fit for purpose is an ongoing struggle. Take your foot off the gas and you might start rolling back.

I'm peering at the adverts in a newsagent's window in east London, and this feels like rolling back. "Double room for a Muslim female or two friends to share with decent Muslim family." As does this. "Double bedroom available. South Indian girl or couple only." And this. "A Nepalese family and we are looking to rent a room for Nepalese people." Backwards, and probably illegal.

I enter the shop to remonstrate. I'm not the first, says the owner – a genial guy of Pakistani origin. "A couple of English people have been in," he admits. "They said: 'How can those ads just be for Indian people.'" He knows the law, and to his credit, he is mortified. I point the ads out. He takes them down. "It's our staff," says his son.

"We know what's allowed, but we're not here all the time." How many of these do you get, I ask. "One a day," his father says. "Africans saying they only want Ghanaians, South Africans saying the only want white South Africans. We tell them to change the ad or we won't take them." Here's one. He produces a strip of paper. Amid scrawl, the "Bangladeshi only" is ruled out with black pen.

The grocery shop window across the road is just as cluttered, but here my experience is different. More dodgy ads – "Boxroom. Sri Lankan and South Indian only." Only this time, the boss is a dunderhead. "I have to run a business," he protests. "If the wrong tenant turns up, they say: 'I wanted a Muslim or a Hindu. I want my money back.' I can't do anything." You can't break the law, I tell him. He argues. Maybe I'll talk to my lawyer, he says finally shuffling away. Yes, I reply.

Before the authorities descend – and they will. That might be a good idea.